The classification of the finite simple groups, also called the enormous theorem, is believed to classify all finite simple groups. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic building blocks of the natural numbers. The Jordan-Hölder theorem is a more precise way of stating this fact about finite groups.

Reading the book has made me look at the bathroom tiles, to notice that all the tiles are of one type — and that you just need to rotate them. What symmetry group is embodied by the tiles? Is the vast majority of commerical household tiles of the same group?